MR-STAT is a framework for obtaining multi-parametric quantitative MR maps using data from single short scans. A single large-scale optimization problem is solved in which spatial localisation of signal and estimation of tissue parameters are performed simultaneously. In previous work, MR-STAT was presented using gradient-balanced sequences with linear, Cartesian readouts. To demonstrate the generic nature of the MR-STAT framework and to explore potentially more efficient acquisition schemes, we extend MR-STAT to non-Cartesian gradient trajectories as well as gradient-spoiled sequences. We compare the our results from golden angle radial, gradient-spoiled acquisitions to low-rank ADMM MRF reconstructions on the same data sets.